Wires A and B are made from the same material | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The energy stored in a stretched wire is given by $W = \frac{1}{2} \frac{F^2 L}{AY}$,where $F$ is the tension,$L$ is the length,$A$ is the cross-s

Vedclass · Accepted Answer

$3 : 4$

Vedclass · Answer

(B) The energy stored in a stretched wire is given by $W = \frac{1}{2} \frac{F^2 L}{AY}$,where $F$ is the tension,$L$ is the length,$A$ is the cross-sectional area,and $Y$ is Young's modulus.Since the wires are made of the same material,$Y_A = Y_B = Y$. The tension $F$ is the same for both.Thus,$W \propto \frac{L}{A}$.Since $A = \pi r^2$,we have $W \propto \frac{L}{r^2}$.Given $L_A = 3L_B$ and $d_A = 2d_B \implies r_A = 2r_B$.Therefore,$\frac{W_A}{W_B} = \frac{L_A}{L_B} 	imes \left(\frac{r_B}{r_A}ight)^2$.Substituting the values: $\frac{W_A}{W_B} = 3 	imes \left(\frac{1}{2}ight)^2 = 3 	imes \frac{1}{4} = \frac{3}{4}$.

Wires $A$ and $B$ are made from the same material. $A$ has twice the diameter and three times the length of $B$. If the elastic limits are not reached,when each is stretched by the same tension,the ratio of energy stored in $A$ to that in $B$ is

Similar Questions

Which of the following sets of quantum numbers belongs to the highest energy orbital?

Which part of the human ear plays no role in hearing as such but is otherwise very much required?

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$, then $k$ is equal to

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

The coefficient of $x^{24}$ in the expansion of $(1+x^2)^{12}(1+x^{12})(1+x^{24})$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module